DIELECTRIC PROPERTIES OF INSULATING MATERIALS 517 



but that in dielectrics this proportionaHty does not in general prevail. 

 The current in a dielectric is complex and heat is developed only by its 

 dissipative component. If the expressions for e' and e" given in (17) 

 and (19) are substituted in (8) we see that when w becomes large by 

 comparison with 1/t, i.e., when 7' becomes 7a,, the imaginary compo- 

 nent of the current reduces to eooco/47r; this is the optical polarization 

 current. If it is subtracted from the total current given by (8), the 

 remaining current contains no imaginary component. This current 

 then develops as much heat in the dielectric as would a current of the 

 same magnitude flowing in a conductor. 



(4) In connection with the foregoing we see that unlike lower values 

 of 7' the infinite-frequency conductivity 700 is a measure of the ease 

 with which electrical charge can be displaced in the material by a unit 

 applied field. This characteristic of 7=0 agrees with our usual concep- 

 tion of the physical basis of the conductivity of an electrolyte or a 

 metal. (We assume in this connection that the optical polarization 

 current e^oijAiir may be neglected in comparison with the current 

 responsible for 7«,. Where this is not the case, appropriate modifica- 

 tions in the above statements are required.) 



(5) It is characteristic of a dielectric that when the charged particles 

 which form part of its structure are displaced by a force of external 

 origin, there is a restoring force tending to return them to their initial 

 positions. On the other hand, in an ideal conductor there are, by 

 definition, no restoring forces of this kind. The above discussion of 

 the model shows that in a dielectric possessing the property of anoma- 

 lous dispersion it is possible to make the influence of the restoring 

 forces on the motion of a bound ion negligible in comparison with that 

 of the applied force by sufficiently increasing the frequency above the 

 value corresponding to the reciprocal of the relaxation-time. This is 

 the condition which prevails when 7' equals 700- Thus at low fre- 

 quencies (oj <3C T^O the part of the dielectric structure which is re- 

 sponsible for anomalous dispersion behaves as a dielectric; whereas at 

 high frequencies (w y^ t"^ it behaves as a conductor. A result of this 

 is that a dielectric exhibiting anomalous dispersion of the simple kind 

 conforming to equation (39) of the preceding paper will behave in an 

 electric circuit like a pure capacity shunted by a pure resistance over 

 the whole of that range of frequencies where e' and 7' are both prac- 

 tically independent of frequency and equal respectively to €00 and 700. 

 Pure ice, for example, behaves in this manner over a considerable range 

 of frequencies. (See Figs. 2 and 4.) 



(6) The average velocity of the bound ion of our model becomes 

 independent of frequency when co is large as compared with l/r. This 



